The following technical report is available from
http://aib.informatik.rwth-aachen.de:
A Dependency Pair Framework for Innermost Complexity Analysis
of Term Rewrite Systems
Lars Noschinski, Fabian Emmes, Jürgen Giesl
AIB 2011-03
We present a modular framework to analyze the innermost runtime
complexity of term rewrite systems automatically. Our method is
based on the dependency pair framework for termination analysis.
In contrast to previous work, we developed a direct adaptation
of successful termination techniques from the dependency pair
framework in order to use them for complexity analysis. By
extensive experimental results, we demonstrate the power of
our method compared to existing techniques.
The following technical report is available from
http://aib.informatik.rwth-aachen.de:
Modular Termination Proofs of Recursive Java Bytecode Programs
by Term Rewriting
Marc Brockschmidt, Carsten Otto, Jürgen Giesl
AIB 2011-02
In earlier work we presented an approach to prove termination of
non-recursive Java Bytecode (JBC) programs automatically. Here,
JBC programs are first transformed to finite termination graphs
which represent all possible runs of the program.
Afterwards, the termination graphs are translated to term
rewrite systems (TRSs) such that termination of the resulting TRSs
implies termination of the original JBC programs. So in this way,
existing techniques and tools from term rewriting can be used to
prove termination of JBC automatically. In this paper, we improve
this approach substantially in two ways:
(1) We extend it in order to also analyze recursive JBC programs.
To this end, one has to represent call stacks of arbitrary
size.
(2) To handle JBC programs with several methods, we modularize our
approach in order to re-use termination graphs and TRSs for the
separate methods and to prove termination of the resulting TRS
in a modular way.
We implemented our approach in the tool AProVE. Our experiments show
that the new contributions increase the power of termination analysis
for JBC significantly.